What is 6/19 plus 8/21?
6/19 plus 8/21 equals 278/399 (or 0.696742 in decimal form). Learn the step-by-step solution to add 6/19 and 8/21 using Least Common Denominator and simplification.
Exact Answer
6/19 + 8/21 = 278/399
Simplified Fraction
278/399
Mixed Number
Proper (278/399)
Decimal Value
0.696742
Percentage
69.6742%
Step-by-Step Solution: 6/19 + 8/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 19 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 19 × 21 = 399.
LCD(19, 21) = 399
Step 2
Convert to Equivalent Fractions with Common Denominator 399
Multiply the numerator and denominator of 6/19 by 21, and multiply the numerator and denominator of 8/21 by 19 so both fractions share the common base 399.
6 × 21/19 × 21 = 126/399 and 8 × 19/21 × 19 = 152/399
Step 3
Add the Numerators
Now add the numerators (126 + 152 = 278) and keep the common denominator 399 unchanged.
126 + 152/399 = 278/399
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 278 and 399 is 1, confirming that 278/399 cannot be reduced further—it is already in its simplest irreducible form.
278/399
Step 5
Decimal & Percentage Representation
Dividing the numerator 278 by denominator 399 produces a repeating decimal (approximately 0.696742, or 69.6742%).
278 ÷ 399 = 0.696742 (69.6742%)
Visual Representation
The diagram below illustrates 6/19 plus 8/21 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 278/399 |
| Mixed Number Form | 278/399 |
| Decimal Form | 0.696742 |
| Percentage | 69.6742% |
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Frequently Asked Questions
What is 6/19 plus 8/21 as a fraction?
6/19 + 8/21 in simplest fraction form is 278/399.
What is 6/19 plus 8/21 as a decimal?
6/19 + 8/21 converted to a decimal is 0.696742.
What is 6/19 plus 8/21 as a percentage?
6/19 + 8/21 expressed as a percentage is 69.6742%.
Does 6/19 plus 8/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 0.696742...) because the denominator contains prime factors other than 2 and 5.